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The correct answer is 明日なの, not 明日. Why is that? My reasoning is that テストが明日を
would mean "the test is performing an action on tomorrow", but we want to
apply を to the whole テストが明日, so we need to turn this phrase into a "noun" by
adding の, and because 明日 itself is a noun, な is needed in between.

Is this correct?


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question
nominalization
テストが（　）を知りませんでした。 - what to put inside parenthesis?


> Is this correct?

Yeah, basically.

Given

> テストが明日を知りませんでした

Then as you say, we get テスト as a subject and 明日 as a direct object, giving us
something like

> The test didn't know tomorrow (???)

Which is generally not a reasonable thing to say.

With the below:

> テストが明日なのを知りませんでした

We have

> (I) didn't know that the test is tomorrow

Where the object of verb is the clause テストが明日なの. The most natural subject here
is an implied "me", mostly because the only reading of the sentence that makes
sense is one in which テストが is part of the subordinate clause.

If having a subordinate clause without an explicit verb makes you
uncomfortable, it may help to think of this as `テストが明日であるのを知りませんでした`, which is
mostly equivalent in terms of meaning. `である` sounds fairly stiff/academic
though so `なの` is much more common.


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answer


If you were asked to put what you didn't know in a sentence (in polite style),
you would say:

> テストは明日です。

It's a sentence with a nominal predicate, meaning it ends with `[N]-です`. (No
action is involved here.) To connect such a sentence to の, you need to add な
as `[N]-なの`.

> ［テストが明日 **な** ］のを知りませんでした。

The same rule applies to a sentence that ends with `[な-Adj]-です`.

> ［テストが簡単 **な** ］のを知りませんでした。

Verbs and い-adjectives, on the other hand, connect directly to の in their
various plain forms.

> 明日テストがあります。
>
> ［明日テストがある］のを知りませんでした。

> テストは難しいです。
>
> ［テストが難しい］のを知りませんでした。

です works like normal verbs in past tense as its past plain form だった connects
directly to の with no connector like な.

> テストは昨日でした。
>
> ［テストが昨日だった］のを知りませんでした。


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